A056979 Number of blocks of {1, 0, 1} in binary expansion of n.

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 1, 1, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 2, 3, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 0, 0, 0, 0, 0, 1, 0

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Comments

a(n) = A213629(n,5) for n > 4. - Reinhard Zumkeller, Jun 17 2012

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• J.-P. Allouche, J. Shallit, The Ring of k-regular Sequences II
• Eric Weisstein's World of Mathematics, Digit Block
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A014082, A056974, A056975, A056976, A056977, A056978, A056979, A056980.

Programs

Haskell

import Data.List (tails, isPrefixOf)
a056979 = sum . map (fromEnum . ([1,0,1] `isPrefixOf`)) .
                    tails . a030308_row
-- Reinhard Zumkeller, Jun 17 2012

Mathematica

a[1] = a[2] = 0; a[n_] := a[n] = If[EvenQ[n], a[n/2], a[(n - 1)/2] + Boole[Mod[(n - 1)/2, 4] == 2]]; Table[a[n], {n, 1, 102}] (* Jean-François Alcover, Oct 22 2012, after Ralf Stephan *)

PARI

a(n) = hammingweight(bitnegimply(bitand(n, n>>2), n>>1));
vector(102, i, a(i))  \\ Gheorghe Coserea, Sep 17 2015

Formula

a(2n) = a(n), a(2n+1) = a(n) + [n congruent to 2 mod 4]. - Ralf Stephan, Aug 22 2003